Critical behavior of fluid interfaces in two dimensions

It is shown that in two dimensions, the capillary-wave theory of the critical interface between fluid phases predicts that the interfacial thickness diverges with an exponent which differs strongly from that given by scaling theory. This is in contrast to the agreement between capillary-wave theory and scaling theory in three dimensions, which is shown to persist in four dimensions. Optical reflectivity measurements may be able to discriminate between capillary-wave and scaling theories in two dimensions, while they cannot in three dimensions.